Image satellite planning is a planning process used to determine the pointing path that an imaging satellite takes as it passes over a set of targets on the ground. In order to take an image of a particular target on the ground, the satellite needs to be pointed in the correct direction, meaning the satellite has a particular attitude. Additionally, in order to take a scanning image over a target, the satellite needs to move at the correct scanning velocity, meaning the satellite has a particular satellite rate (the angular velocity of the satellite, also called the attitude rate or scan rate). For example, the scan rate may be about 0.75 degrees per second. The desired attitude and attitude rate for the imaging pass are determined based on the location and size of the image on the ground, and other factors regarding the image being taken. Then, a maneuver is calculated in order to move the satellite from its initial attitude and attitude rate to the desired attitude and attitude rate at the correct time for the imaging pass.
In order to execute this maneuver and change the attitude of the satellite, the satellite has some type of onboard attitude control system. One type of onboard attitude control system includes a set of control moment gyroscopes (“CMG”) as well as a command generator, a sensor package, and a set of control laws. A satellite needs at least three separate CMG's in order to have complete control over its attitude in three-dimensional space. An example of a single CMG 12 is shown in FIG. 1. The CMG includes a rotor such as wheel 14 that spins about an axis 16. The rotor 14 is supported by a frame 18 that is mounted to the satellite through a gimbal (a pivoted support that allows the frame 18 to rotate about axis 20). The angular momentum vector H of the rotor 14 is parallel to the axis 16. The frame 18 can be rotated about a second axis 20, which is perpendicular to the axis 16 and angular momentum vector H. The angle of rotation of the frame 18 about the axis 20 is the gimbal angle δ.
The satellite includes at least three CMG's, and often includes up to six. The number of CMG's on the satellite is referred to as “n” CMG's. The CMG's are mounted to the satellite such that the planes defined by the axes 16 and 20 of each CMG are angled with respect to each other. Each one of the CMG's can be rotated about its axis 20 to a particular gimbal angle δ. The gimbal angles of all n CMG's may be referred to as the set or vector of gimbal angles. At one set of gimbal angles, the satellite has no angular momentum, as the sum of all of the angular momentum vectors H of the n CMG's is zero. At this position, each gimbal angle δ of each CMG may be defined as zero. If one of the frames 18 is rotated to change the gimbal angle δ, then the sum of the angular momentum vectors H is no longer zero, and angular momentum is imparted to the satellite.
At any set of non-zero gimbal angles δ, the satellite is rotating about some axis, with an angular momentum and satellite rate. While the gimbal angles δ are changing, the satellite is accelerating. While the gimbal angles δ are constant and non-zero, the satellite is rotating. When the gimbal angles are constant and zero, the satellite is not rotating. The satellite's angular momentum vector H corresponds to one or more sets of gimbal angles. For angular momentum vectors below the maximum angular momentum envelope, several different sets of gimbal angles can provide the same angular momentum H to the satellite. A maximum angular momentum vector has a unique set of gimbal angles. The gimbal angle vectors 8 and corresponding angular momentum vectors H can be mapped to each other.
In order for the satellite to image a set of targets on the ground, the attitude of the satellite has to be controlled in order to point the satellite in the correct direction at the correct time and with the correct scanning velocity (satellite rate). An example set of targets 22 on the ground is shown in FIG. 2. The satellite follows a pointing path 14 to image a select subset of targets 22a, 22b, 22c, etc, during the satellite's pass overhead. Between each target 22a, 22b, 22c, the satellite executes a maneuver to reorient the satellite to point in the correct direction to image the next target.
There are various prior art methods for calculating this attitude-changing maneuver. One prior art method calculates the maneuver in angular momentum space, meaning that the satellite attitude, rate, and acceleration are used to determine the desired trajectory, and the CMG's are rotated as needed to initiate satellite rotation along this trajectory. The shortest distance in angular momentum space is an Eigen axis maneuver, where the satellite is rotated about a single vector. The CMG's are then further rotated as needed to increase the magnitude of rotation about this vector until the final angular momentum is reached.
However, this prior art method does not provide the minimum time maneuver for moving the satellite to the desired imaging attitude and attitude rate. The present invention provides a method for commanding the CMG's and maneuvering the satellite to the desired attitude and attitude rate with a shorter-duration maneuver. As a result, less time is required for each maneuver, and more time is available in the imaging pass for taking images of the targets.